We define very large multi-objective optimization problems to be multiobjective optimization problems in which the number of decision variables is greater than 100,000 dimensions. This is an important class of problems as many real-world problems require optimizing hundreds of thousands of variables. Existing evolutionary optimization methods fall short of such requirements when dealing with problems at this very large scale. Inspired by the success of existing recommender systems to handle very large-scale items with limited historical interactions, in this paper we propose a method termed Very large-scale Multiobjective Optimization through Recommender Systems (VMORS). The idea of the proposed method is to transform the defined such very large-scale problems into a problem that can be tackled by a recommender system. In the framework, the solutions are regarded as users, and the different evolution directions are items waiting for the recommendation. We use Thompson sampling to recommend the most suitable items (evolutionary directions) for different users (solutions), in order to locate the optimal solution to a multiobjective optimization problem in a very large search space within acceptable time. We test our proposed method on different problems from 100,000 to 500,000 dimensions, and experimental results show that our method not only shows good performance but also significant improvement over existing methods.

翻译：我们将超大规模多目标优化问题定义为决策变量数量超过100,000维的多目标优化问题。由于许多实际问题需要优化数十万个变量，这是一类重要的问题。现有进化优化方法在处理这种超大规模问题时无法满足要求。受现有推荐系统在有限历史交互下成功处理超大规模项目的启发，本文提出一种名为"基于推荐系统的超大规模多目标优化"（VMORS）的方法。该方法的核心理念是将所定义的超大规模问题转化为可由推荐系统处理的问题。在该框架中，解被视作用户，不同进化方向则是待推荐的项目。我们采用汤普森采样为不同用户（解）推荐最合适的项目（进化方向），从而在可接受时间内于超大规模搜索空间中定位多目标优化问题的最优解。我们在从100,000维到500,000维的不同问题上测试了所提方法，实验结果表明，该方法不仅表现出良好性能，而且相较于现有方法具有显著改进。